The trick to this recipe is the technique. If you don't use a heavy duty mixer (to cream the butter, sugar, and eggs, as directed) and don't let the cookie dough rest in the refrigerator overnight, these are just regular chocolate chip cookies.
Measure all ingredients. Let butter warm to room temperature. Sift the dry ingredients together a few times.
Beat butter in mixing bowl of a heavy duty mixer (such as a Kitchen Aid 4½ or 5-quart mixer) with flat (paddle) beater at medium speed until it is lighter and clings to bowl (30-45 seconds). Keeping beater at medium speed add both sugars in a steady stream. Continue to cream butter and sugars for 4-5 minutes, scraping down bowl twice. When done the mixture will be light in color and fluffy in appearance.
Whisk eggs with vanilla in small bowl and add to butter and sugar mixture, keeping beater on medium speed. Be careful to pour in the eggs very slowly. It should take 3-4 minutes to add the eggs. The mixture then appears fluffy, looking like whipped cream cheese. (This is the "creaming method" for making a butter cake, which I learned from Flo Braker's The Simple Art of Perfect Baking.)
Put beater on slowest speed and add dry ingredients. As soon as the dry ingredients are incorporated, add chocolate chips and walnuts. Leave beater on lowest speed for a few seconds to mix it all together.
(The best chocolate chips around are from the Guittard Chocolate Company, but you cannot find these at all grocery stores. Sometimes I replace ½ of the chocolate chips with either peanut butter chips, raspberry chips, or mint chips. The latter two I often find in the grocery store around Christmas.)
Make into golf ball sized balls and place on cookie sheet right next to each other. (I use an ice cream scoop to measure each cookie.) This should make about 30-35 cookies. (I put 5 rows of 7 cookies on a 17-inch by 11-inch cookie sheet.) Put in fridge overnight or for at least 6 hours, covered. Remove and let warm to room temperature (30 min.). Put cookie balls on baking sheet to bake. Flatten a little to resemble a hockey puck, about ¾-inch high. Make edges go straight up and down. Make a slight depression in center with finger.
Bake at 400 degrees, 8-10 minutes. Edges should be golden brown but center 1-inch pale. Let sit at room temperature 5 minutes before taking off baking pan.